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Ben 10: Hypertimeline and Uncountable Branching Timelines

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Okay. And which staff members think what here other than Firestorm808?
 
Branching Timelines (Low 1-C)
"Paradox: As Gwen guessed, cross-time is made up of parallel versions of the history we know. There are hundreds of them... a world where Gwen found the Omnitrix, a world where albedo turned to alien x and was trapped motionless for nearly a year, a world where you didn't have to destroy the Omnitrix to defeat Vilgax.

Ben 10K: Et cetera.

Paradox: Ad infinitum.”

-Paradox and Ultimate Ben 10k

With Paradox and Ben 10K, Paradox listed the alternate timelines are parallel versions of history we know, referring prime universe being the history they know and alternative universe to be parallel versions of it, ending the conversation with ad infinitum, suggesting that existing timelines branch forever, again and again making this a continuous process of branching.

“Think of time and space as this tree. Down here is when you were 10 years old. Right here is now. Up here is when you'll 30 be years old. The trunk is the main timeline. These branches represent alternate timelines, where reality literally branches off and becomes a different timeline, each containing its own Ben Tennyson.”

-Paradox to NW Ben

"We are near the beginning of the Ben Prime Timeline. The trunk of the Ben Tennyson tree from which all other Ben realities diverge."

-Paradox to NW Ben

All the other universes diverge as a result of different possible outcomes of Prime Ben's reality.

Here Paradox divides Prime Ben's Universe into three snapshots which are 10, 16 and 30 year old where each snapshot of Prime Ben's reality branches off and becomes a different timeline. Each alternative timeline also branches further as seen in the scan below.

While this tree was an easier explanation for NW Ben, there are some Good examples of other snapshots branching which can be seen over here. The main trunk has all snapshots of Ben Prime's Timeline which is a 2-A structure. And the alternate timelines branch as a result of another outcome of the main trunk. Then these alternate timelines branchfurther into more alternate timelines. This process continues ad infinitum which makes the total number of timelines equal to 2-A×2-A×2-A×2-A×.....ℵ0 times = ℵ0^ℵ0  which is numerically greater than ℵ1.
 
Hellformer said:
Branching Timelines (Low 1-C)
"Paradox: As Gwen guessed, cross-time is made up of parallel versions of the history we know. There are hundreds of them... a world where Gwen found the Omnitrix, a world where albedo turned to alien x and was trapped motionless for nearly a year, a world where you didn't have to destroy the Omnitrix to defeat Vilgax.

Ben 10K: Et cetera.

Paradox: Ad infinitum.”

-Paradox and Ultimate Ben 10k

With Paradox and Ben 10K, Paradox listed the alternate timelines are parallel versions of history we know, referring prime universe being the history they know and alternative universe to be parallel versions of it, ending the conversation with ad infinitum, suggesting that existing timelines branch forever, again and again making this a continuous process of branching.

“Think of time and space as this tree. Down here is when you were 10 years old. Right here is now. Up here is when you'll 30 be years old. The trunk is the main timeline. These branches represent alternate timelines, where reality literally branches off and becomes a different timeline, each containing its own Ben Tennyson.”

-Paradox to NW Ben

"We are near the beginning of the Ben Prime Timeline. The trunk of the Ben Tennyson tree from which all other Ben realities diverge."

-Paradox to NW Ben

All the other universes diverge as a result of different possible outcomes of Prime Ben's reality.

Here Paradox divides Prime Ben's Universe into three snapshots which are 10, 16 and 30 year old where each snapshot of Prime Ben's reality branches off and becomes a different timeline. Each alternative timeline also branches further as seen in the scan below.

While this tree was an easier explanation for NW Ben, there are some Good examples of other snapshots branching which can be seen over here. The main trunk has all snapshots of Ben Prime's Timeline which is a 2-A structure. And the alternate timelines branch as a result of another outcome of the main trunk. Then these alternate timelines branchfurther into more alternate timelines. This process continues ad infinitum which makes the total number of timelines equal to 2-A×2-A×2-A×2-A×.....ℵ0 times = ℵ0^ℵ0  which is numerically greater than ℵ1.
Click to expand...

NXCHT.66 said:
@Hellformer I guess it can be applied. Can you summarize what changes will be made?
Click to expand...
Lemme know if this explanation is correct and enough or do we need changes
 
Hellformer said:
This process continues ad infinitum which makes the total number of timelines equal to 2-A×2-A×2-A×2-A×.....ℵ0 times = ℵ0^ℵ0  which is numerically greater than ℵ1.
Click to expand...

First off, continuing a process ad infinitum of multiplication like that doesn’t even guarantee it’s remotely comparable to ℵ0^ℵ0.

For example, take the collection {2^n|n in N}. This is the family {1, 2, 2x2, 2x2x2, 2x2x2x2, …}.This process of multiplication continues ad infinitum, but the union of that family of sets is not 2^ℵ0, and, in fact, is countable. The infinite Cartesian product {0, 1}x{0, 1}x{0, 1}x… is uncountable, but that’s not necessarily the case for this example.

Second off, ℵ0^ℵ0>ℵ1 is equivalent to rejecting the continuum hypothesis, which is independent of ZFC.
 
Eclipso said:
First off, continuing a process ad infinitum of multiplication like that doesn’t even guarantee it’s remotely comparable to ℵ0^ℵ0.

For example, take the collection {2^n|n in N}. This is the family {1, 2, 2x2, 2x2x2, 2x2x2x2, …}.This process of multiplication continues ad infinitum, but the union of that family of sets is not 2^ℵ0, and, in fact, is countable. The infinite Cartesian product {0, 1}x{0, 1}x{0, 1}x… is uncountable, but that’s not necessarily the case for this example.

Second off, ℵ0^ℵ0>ℵ1 is equivalent to rejecting the continuum hypothesis, which is independent of ZFC.
Click to expand...
I mean one yeah you could say that there is no cardinality between ℵ0 and ℵ1, ℵ1 and ℵ2, so on and so forth according to the continuum hypothesis.
So I'd change the reasoning to-
The total number of timelines branching ad infinitum would be same as ℵ1 which would be equal to the cardinality of the set of all possible real outcomes of the main trunk.

Basically my argument for the tree is similar to that of the MCU branching which is currently 5-D for these reasons:
With this we can conclude that all of the uncountable infinite timelines that branched out indefinitely from the Sacred Timeline at least contain an infinite number of universes, realities and dimensions, endless possibilities where every passing/singular moment can branch out into infinite realities and possibilities, making each single branch a 2-A structure which in turn can branch out into uncountable infinite 2-A structures on its own, and so on ad infinitum with each single branch.
 
Hellformer said:
I mean one yeah you could say that there is no cardinality between ℵ0 and ℵ1, ℵ1 and ℵ2, so on and so forth according to the continuum hypothesis.
Click to expand...

Whether CH is true or not is independent of that. It is a theorem of ZF that there is no cardinality between aleph x and aleph (x+1).

CH is the statement that aleph 1 is equal to Beth 1.
 
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